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A Notion of Equivalence for Stochastic Petri Nets.

Buchholz, Peter

In: Proceeding of the 16th International Conference on Application and Theory of Petri Nets, Turin, June 1995., pages 161-180. 1995.

Abstract: Equivalence is a central concept for the qualitative analysis of dynamic systems. Several different notions of equivalence preserving qualitative properties of a system appeared in the literature on Petri nets (PNs). If apart from qualitative also quantitative aspects of a system should be analysed, then there exists the class of stochastic Petri nets (SPNs) extending PNs by associating exponentially distributed delays with transitions. However, relations to define equivalence of systems according to quantitative aspects in a systematic way have not been published. This paper proposes a first approach to define quantitative equivalence of SPNs. It is shown that one of the presented relations is an extention of bisimulation equivalence for nets without time. Furthermore, quantitative equivalence is a congruence according to the parallel composition of SPNs as introduced in this paper. For the proposed quantitative equivalence an algorithm to compute the minimal equivalent realisation of a SPN on marking space level is presented.

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